Computation of the Amplitude of Stress Singular Terms for Cracks and Reentrant Corners

Abstract

The theoretical basis and performance characteristics of two new methods for the computation of the coefficients of the terms of asymptotic expansions at reentrant corners from finite-element solutions are presented. The methods, called the contour integral method (CIM) and the cutoff function method (CFM), are very efficient: the coefficients converge to their true values as fast as the strain energy, or faster. In order to make the presentation as simple as possible, we assume that the elastic body is homogeneous and isotropic, is loaded by boundary tractions only, and, in the neighborhood of the reentrant corner, has stress-free boundaries. The methods described herein can be adapted to cases without such restrictions.

Superconvergent extraction of flux intensity factors and first derivatives from finite element solutions

“…One of the most efficient ways for extracting the GSIFs in a superconvergent manner is by indirect extraction procedure using the CIM and the CFM presented in [7,91. These efficient procedures use specially constructed extraction functions.…”

The solution of axisymmetric problems near singular points and computation of stress intensity factors

“…One of the most efficient methods to extract the GSIFs for cracked configurations is the contour integral method (CIM) first introduced in [7], and incorporated for 2-D elasticity in [8]. For detailed discussion on the CIM we refer to [7][8][9], where it has been shown that the method yield superconvergent results.…”

An expert-system-like feedback approach in the hp-version of the finite element method

“…2 For the way to compute stress intensity factors we refer to [17], and [18]. It has been shown that the optimal number n of layers of elements increases with the polynomial degree p, that the optimal ratio of the geometric mesh is independent of the strength of the singularity, p, and the number n of layers and has a magnitude of .15.…”

“…In two numerical examples we will show the steps of the expert system as shows mode 1 stress distribution given, for example, in [18]. The solution * has singular behaviour at the reentrant corner.…”